b. 6x(x - 5) - x(6x + 3)

= x(6x - 30) - x(6x + 3)

= x(6x - 30 - 6x - 3)

= x(-33)

= -33x

\(1,\\ a,=-35x^5y^4z\\ b,=6x^2-30x-6x^2-3x=-33x\\ c,=x^3-9x^2-2x^2+18x-x+9=x^3-11x^2+17x+9\\ 2,\\ A\left(x\right)+B\left(x\right)=10-2x+4x^3-5x^2-10x^3-5x+6x^2-20\\ =-6x^3+x^2-7x-10\\ A\left(x\right)-B\left(x\right)=10-2x+4x^3-5x^2+10x^3+5x-6x^2+20\\ =14x^3-11x^2+3x+30\\ 3,\\ a,M\left(x\right)=5x+20=0\\ \Leftrightarrow x=-4\\ b,N\left(x\right)=100x^2-49=0\\ \Leftrightarrow\left(10x-7\right)\left(10x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{10}\\x=-\dfrac{7}{10}\end{matrix}\right.\\ c,P\left(x\right)=3x-15=0\\ \Leftrightarrow x=5\)

Bài 1;

a)\(5x^3yz.\left(-7x^2y^3\right)=-35.x^5y^4z\)

b)\(6x\left(x-5\right)-x\left(6x+3\right)=6x^2-30x-6x^2-3x=-33x\)

c) \(\left(x-9\right)\left(x^2-2x-1\right)=x^3-2x^2-x-9x^2+18x+9=x^3-11x^2+17x+9\)

\(5x\left(x-3\right)-x^2+6x-9\\ =5x\left(x-3\right)-\left(x^2-6x+9\right)\\ =5x\left(x-3\right)-\left(x-3\right)^2\\ =\left(x-3\right)\left(5x-x+3\right)\\ =\left(x-3\right)\left(4x+3\right)\)

a. 2x\(^2\)-8=0

2x\(^2\)=8

x\(^2\)=4

x=2

b.3x\(^3\)-5x=0

x(3x\(^2\)-5)=0

\(\left[{}\begin{matrix}x=0\\x^2-5=0\end{matrix}\right.\)⇔\(\left[{}\begin{matrix}x=0\\x^2=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=^+_-\sqrt{5}\end{matrix}\right.\)

c.x+3x-4=0\(^{\left(\cdot\right)}\)

đặt t=x\(^2\) (t>0)

ta có pt: t\(^2\)+3t-4=0 \(^{\left(1\right)}\)

thấy có a+b+c=1+3+(-4)=0 nên pt\(^{\left(1\right)}\) có 2 nghiệm

t\(_1\)=1; t\(_2\)=\(\dfrac{c}{a}\)=-4

khi t\(_1\)=1 thì x\(^2\)=1 ⇒x=\(^+_-\)1

khi t\(_2\)=-4 thì x\(^2\)=-4 ⇒ x=\(^+_-\)2

vậy pt đã cho có 4 nghiệm x=\(^+_-\)1; x=\(^+_-\)2

d)3x\(^2\)+6x-9=0

thấy có a+b+c= 3+6+(-9)=0 nên pt có 2 nghiệm

x\(_1\)=1; x\(_2\)=\(\dfrac{c}{a}=\dfrac{-9}{3}=-3\)

e. \(\dfrac{x+2}{x-5}+3=\dfrac{6}{2-x}\)  (ĐK: x#5; x#2 )

⇔\(\dfrac{\left(x+2\right)\left(2-x\right)}{\left(x-5\right)\left(2-x\right)}+\dfrac{3\left(x+2\right)\left(2-x\right)}{\left(x-5\right)\left(2-x\right)}\)=\(\dfrac{6\left(x-5\right)}{\left(x-5\right)\left(2-x\right)}\)

⇒2x - x\(^2\) + 4 - 2x + 6x - 6x\(^2\) + 12 - 6x - 6x +30 = 0

⇔-7x\(^2\) - 6x + 46=0

Δ'=b'\(^2\)-ac = (-3)\(^2\) - (-7)\(\times\)46= 9+53 = 62>0

\(\sqrt{\Delta'}=\sqrt{62}\)

vậy pt có 2 nghiệm phân biệt

x\(_1\)=\(\dfrac{-b'+\sqrt{\Delta'}}{a}=\dfrac{3+\sqrt{62}}{-7}\)

x\(_2\)=\(\dfrac{-b'-\sqrt{\Delta'}}{a}=\dfrac{3-\sqrt{62}}{-7}\)

vậy pt đã cho có 2 nghiệm x\(_1\)=.....;x\(_2\)=......

câu g làm tương tự câu c

\(=\dfrac{6x}{\left(x-3\right)\left(x+3\right)}-\dfrac{9+5x}{x-3}+\dfrac{x}{x+3}\)

\(=\dfrac{6x-\left(5x+9\right)\left(x+3\right)+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{x^2+3x-5x^2-15x-9x-27}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{-4x^2-21x-27}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{-\left(4x^2+12x+9x+27\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{-4x-9}{x-3}\)

a) \(\frac{4x+3}{6x-4}+\frac{5x-9}{6x-4}\)

\(=\frac{4x+3+5x-9}{2\left(3x-2\right)}=\frac{9x-6}{2\left(3x-2\right)}\)

\(=\frac{3\left(3x-2\right)}{2\left(3x-2\right)}=\frac{3}{2}\)

b) \(\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{x^2-1}\)

\(=\frac{2\left(x+1\right)+3\left(x-1\right)-4x+2}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{x+1}{\left(x-1\right)\left(x+1\right)}=\frac{1}{x-1}\)

a) \(\frac{4x+3}{6x-4}+\frac{5x-9}{6x-4}\)

\(=\frac{4x+3+5x-9}{6x-4}\)

\(=\frac{9x-6}{6x-4}\)

\(=\frac{3.\left(3x-2\right)}{2.\left(3x-2\right)}\)

\(=\frac{3}{2}.\)

b) \(\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{x^2-1}\)

\(=\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{\left(x-1\right).\left(x+1\right)}\)

\(=\frac{2.\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}+\frac{3.\left(x-1\right)}{\left(x-1\right).\left(x+1\right)}-\frac{4x-2}{\left(x-1\right).\left(x+1\right)}\)

\(=\frac{2x+2}{\left(x-1\right).\left(x+1\right)}+\frac{3x-3}{\left(x-1\right).\left(x+1\right)}+\frac{-\left(4x-2\right)}{\left(x-1\right).\left(x+1\right)}\)

\(=\frac{2x+2+3x-3-4x+2}{\left(x-1\right).\left(x+1\right)}\)

\(=\frac{x+1}{\left(x-1\right).\left(x+1\right)}\)

\(=\frac{1}{x-1}.\)

Chúc bạn học tốt!

6x³ - 7x² + 5x - 2
= 6x³ - 4x² - 3x² + 2x + 3x - 2
= 6x²(x - 2/3) - 3x(x - 2/3) + 3(x - 2/3)
= (x - 2/3)(6x² - 3x + 3)
= 3(x - 2/3)(2x² - x + 1)

4x³ + 5x² + 10x - 12
= 4x³ - 3x² + 8x² - 6x + 16x - 12
= 4x²(x - 3/4) + 8x(x - 3/4) + 16(x - 3/4)
= (x - 3/4)(4x² + 8x + 16)
= 4(x - 3/4)(x² + 2x + 4)

4x³ - 7x² - x + 3
= 4x³ - 3x² - 4x² + 3x - 4x + 3
= 4x²(x - 3/4) - 4x(x - 3/4) - 4(x - 3/4)
= (x - 3/4)(4x² - 4x - 4)
= 4(x - 3/4)(x² - x - 1)

4x³ - 5x² + 6x + 9
= 4x³ + 3x² - 8x² - 6x + 12x + 9
= 4x²(x + 3/4) - 8x(x + 3/4) + 12(x + 3/4)
= (x + 3/4)(4x² - 8x + 12)
= 4(x + 3/4)(x² - 2x + 3)

3x³ - 5x² + 5x - 2
= 3x³ - 2x² - 3x² + 2x + 3x - 2
= 3x²(x - 2/3) - 3x(x - 2/3) + 3(x - 2/3)
= (x - 2/3)(3x² - 3x + 3)
= 3(x - 2/3)(x² - x + 1)